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The quadratic convergence of the topological epsilon algorithm for systems of nonlinear equations

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Abstract

In this work we consider the topological epsilon algorithm for solving systems of nonlinear equations. In section 2, a sufficient condition for its quadratic convergence is given. In section 3, some geometrical remarks about this condition are made.

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References

  1. C. Brezinski,Accélération de la Convergence en Analyse Numérique, Lecture Notes in Mathematics 584 (Springer, Berlin, 1977).

    Google Scholar 

  2. C. Brezinski, Other manifestations of the Schur complement, Lin. Alg. Appl. 111 (1988) 231–247.

    Article  Google Scholar 

  3. E. Geleker, On the solution of systems of equations by the epsilon algorithm of Wynn, Math. Comp. 26 (1972) 427–436.

    Google Scholar 

  4. K. Jbilou and H. Sadok, Some results about vector extrapolation methods and related fixed point iterations, J. Comput. Appl. Math. 36 (1991) 385–398.

    Article  Google Scholar 

  5. A. Sidi, W.F. Ford and D.A. Smith, Acceleration of convergence of vector sequences, SIAM J. Numer. Anal. 23 (1986) 178–196.

    Article  Google Scholar 

  6. S. Skelboe, Computation of the periodic steady-state response of nonlinear networks by extrapolation methods, IEEE Trans. Circuits Syst. CS-27 (1980) 161–175.

    Article  Google Scholar 

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  1. Laboratoire d'Analyse Numérique et d'Optimisation, UFR IEEA, Université des Sciences et Technologies de Lille, 59655, Villeneuve d'Ascq Cedex, France

    Hervé Le Ferrand

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  1. Hervé Le Ferrand
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Le Ferrand, H. The quadratic convergence of the topological epsilon algorithm for systems of nonlinear equations. Numer Algor 3, 273–283 (1992). https://doi.org/10.1007/BF02141936

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  • DOI: https://doi.org/10.1007/BF02141936

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